# Unbias estimators and MSE

**Question description**

Question 4

Let x₁, x₂, …xₓ be a random sample of n i.i.d. observations following the Poisson distribution with parameter (mean) ϴ such that E(Xₐ) = ϴ. Consider three estimators of ϴ given as:

ϴ₁ = X, ϴ₂ = X₁, ϴ₃ = (x₁ + 2x₂)/3

i.) Show that all the three estimators are unbiased

ii.) Calculate which of three has the least Variance

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